Question: Multiply the following complex numbers: $({2-3i}) \cdot ({-3-3i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({2-3i}) \cdot ({-3-3i}) = $ $ ({2} \cdot {-3}) + ({2} \cdot {-3}i) + ({-3}i \cdot {-3}) + ({-3}i \cdot {-3}i) $ Then simplify the terms: $ (-6) + (-6i) + (9i) + (9 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -6 + (-6 + 9)i + 9i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -6 + (-6 + 9)i - 9 $ The result is simplified: $ (-6 - 9) + (3i) = -15+3i $